1. Field of the Invention
The present invention relates to a vector control unit for an induction motor connected with an inverter, the motor being not only electrically driven but also working in a regenerative condition.
2. Description of the Related Art
A slip frequency control method characterized by both excellent responsiveness and accuracy in control has been known as a variable speed control method for an induction motor. Particularly, a vector control method which can provide responsiveness equivalent to that of a D.C. motor, by controlling a primary current of the induction motor, dividing it into an excitation current and a torque current, and controlling a secondary magnetic flux and the torque current in such a way that their directions are constantly kept in a perpendicular relationship to each other, has been put into force. Recently, a speed sensor has been removed from the method (hereinafter referred to as a PG-less method) and the method has been improved through simplification and improving resistance against adverse environmental conditions.
A PG-less induction motor control unit usually comprises, as shown in FIG. 1, a converter unit which consists of a diode and a capacitor and which converts an electric current from an A.C. source to D.C., a voltage type PWM inverter 1 consisting of an inverter unit for generating A.C. voltage by modulating voltage commands of U-, V-, and W-phase output from a current controller to PWM signals by means of a switching element such as a thyristor or IGBT; electric current detectors 10.sub.1, 10.sub.2, 10.sub.3 for detecting electric currents which flow in U-, V-, and W-phases, respectively, of an induction motor 2; a voltage detector 11 for detecting voltages between two of the U-, V-, and W-phases; a vector control unit 3 for performing vector control; and a command generator 19.
FIG. 2 is a block diagram showing the vector control unit 3 shown in FIG. 1.
The vector control unit 3 is composed of a coefficient meter 4; integrator 5; a function generator 6 which inputs phase .theta..psi.* and generates exp (j.theta..psi.*), i.e., cos .theta..psi.*+jsin .theta..psi.*; a two-phase/three-phase converter 7 which converts a vector having components in the direction of a magnetic flux (hereinafter referred to as a "d axis") and in the direction perpendicular thereto (hereinafter referred to as a "q axis") into a vector having components in the directions of the U-, V-, and W-phases which have phase differences of 120.degree. from one another; a vector operation unit 8 for performing the operation of a vector of r=.alpha.+j.beta. which represents a d-axis component .alpha. and a q-axis component .beta., that is, an amplitude .vertline.r.vertline.=(.alpha..sup.2 +.beta..sup.2).sup.1/2 and a phase tan.sup.-1 (.beta./.alpha.); a vector rotator 9 which inputs vector r and exp (j.theta..psi.*) and arranges its phase to .theta..psi.*+tan.sup.-1 (.beta./.alpha.); a magnetic flux operation unit 12 for detecting a magnetic flux and a torque current by using a primary voltage vector v.sub.l obtained from a voltage detector 11 and a primary current vector i.sub.1 obtained from the current detectors 10.sub.1, 10.sub.2, 10.sub.3 ; a velocity presuming unit 13 for presuming an electrical angular velocity of a rotor by using a torque current detection value I.tau. obtained by the magnetic flux operation unit 12 and a torque current command I.tau.*; a magnetic flux command generator 14 which performs field-weakening control based on the magnitude of the electrical angular velocity of the rotor; subtracters 15.sub.1, 15.sub.2 ; a velocity controller 16 for eliminating the error between an angular velocity command .omega.r* from a command generator 19 and a presumed angular velocity .omega.r to perform PI control; a magnetic flux controller 17 for eliminating the magnetic flux error .DELTA..psi..sub.2 between a magnetic flux command .psi..sub.2 * and a detected magnetic flux .psi..sub.2 to perform PI control; electric current controllers 18.sub.1, 18.sub.2, 18.sub.3 provided for every U-, V-, and W-phase for eliminating the error between a command value and a detected value of a primary current to perform P control; subtracters 20.sub.1 to 20.sub.5 ; and an adder 21. The torque current command I.tau.* is obtained by dividing a torque command T* to be acquired as an output of the velocity controller 16 by the magnetic flux command .psi..sub.2 * to be obtained as an output of the magnetic flux command generator 14. An excitation current command I.psi.* is obtained as an output of the magnetic flux controller 17.
The operation of the present conventional example will next be described.
When motor constants are expressed by an asymmetrical T type equivalent circuit shown in FIG. 3, the relation between the voltage and the electric current of the induction motor 2 is given by expression (1) in a static coordinate system. ##EQU1## R: resistance of each phase L.sub.l, M: self-inductance and mutual inductance
l: total leakage inductance (=L.sub.l -M) PA1 .omega..sub.r : angular velocity PA1 p: differential operator PA1 subscript.sub.1,2 : primary and secondary PA1 P: number of motor poles
Further, secondary interleakage magnetic flux .psi..sub.2 and an excitation current i.sub..psi. are represented by expression (2) and (3), respectively. EQU .psi..sub.2 =M(i.sub.1 +i.sub.2) (2) EQU i.sub..psi. =i.sub.1 +i.sub.2 ( 3)
Expression (1) is developed into expressions (4) and (5) by using expressions (2) and (3). EQU v.sub.l =(R.sub.1 +l.multidot.p).multidot.i.sub.1 +p.multidot..psi..sub.2( 4) EQU O=R.sub.2 .multidot.i.sub.2 +(p-j.omega..sub.r).multidot..psi..sub.2( 5)
Next, when a unit magnetic flux vector is represented by .THETA..sub..psi. on a magnetic flux rotating coordinate system, a primary current i.sub.1 and a secondary current i.sub.2 are represented by expressions (6) and (7), respectively. EQU i.sub.1 =(I.sub..psi. +jI.tau.).multidot..THETA..sub..psi. ( 6) EQU i.sub.2 =-(1/R.sub.2).multidot.{p.multidot..psi..sub.2 +j(.omega..sub..psi. -.omega..sub.r).multidot..psi..sub.2 }.multidot..THETA..sub..psi.( 7)
where, .THETA..sub..psi. =exp(j.theta..sub..psi.), .theta..sub..psi. : angle of magnetic flux vector, .omega..sub..psi. : magnetic flux angular velocity.
In expression (6), the operation of the commands I.sub..psi. +jI.sub..tau. and .THETA..sub..psi. is performed by the vector operation unit 8 and by the function generator 6, respectively. The vector rotator 9 inputs these two data values, performs the operation of a primary current command i.sub.1 *, and outputs it as a command corresponding to expression (6).
Further, the relation between the torque current command I.tau.* and a slip angular velocity command .omega..sub.s * is represented by the next expression (8), and its operation is executed by the divider 15.sub.2 and the coefficient meter 4. EQU .omega..sub.s *=R.sub.2 *.multidot.I.tau.*/.psi..sub.2 ( 8)
An angle command .theta..psi.* of a magnetic flux vector is obtained from expression (9) by integrating the sum of a presumed angular velocity .omega.r output from the velocity presuming unit 13 and the slip angular velocity command .omega.s* obtained from expression (8) by using integrator 5. EQU .theta..psi.*=.intg..omega..psi.*dt=(.omega.r.omega.s*)/p (9)
The primary current command i.sub.1 * output from the vector rotator 9 is converted into each current of U-, V-, and W-phase by the two-phase/three-phase converter 7, and the differences between respective electric currents of the U-, V-, and W-phases and the detected values of phase currents detected by the electric current detectors 10.sub.1, 10.sub.2, 10.sub.3 are inputted into electric current controllers 18.sub.1, 18.sub.2, 18.sub.3, respectively, following which the P-controlled results of the above inputted values are sent out to the voltage type PWM inverter 1 as voltage commands thereto. The voltage type PWM inverter 1 modulates these voltage commands to PWM signals to output to the induction motor 2. In addition, voltages between two of the U-, V-, and W-phase are detected by the voltage detector 11 and inputted into the magnetic flux operation unit 12 together with the detected value of the primary electric current. The magnetic flux operation unit 12 performs the operation of expression (10) for obtaining the magnetic flux vector .psi..sub.2 by compensating a voltage drop due to the primary resistance and leakage inductance from the integral value of an inputted primary voltage v.sub.l, and performs the operation of expression (11) for obtaining a torque .tau.. ##EQU2## Im: imaginary part operation mark .psi..sub.2 : conjugate multiple vector of .psi..sub.2
After detecting the amplitude of .psi..sub.2 of expression (10) as the magnetic flux detection value .psi..sub.2, the torque current detection value I.tau. is obtained by dividing expression (11) by .psi..sub.2.
In this way, the PG-less vector control is performed. With the above conventional technique, however, there has been a problem that, when a load is applied to the induction motor while it is being operated at a low speed (a regenerative condition), the absolute value of the magnetic flux angular velocity .omega..psi. is reduced, thereby lowering the accuracy of magnetic flux detection by the vector control unit and reducing the operational stability of the vector control unit and also causing the unit to tend to lose synchronism of operation.